{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T07:15:30Z","timestamp":1760426130772,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,4,28]],"date-time":"2023-04-28T00:00:00Z","timestamp":1682640000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Colocated multiple-input multiple-output (MIMO) radar can transmit a group of distinct waveforms via its colocated transmit antennas and the waveform diversity leads to several advantages in contrast to conventional phased-array radar. The performance depends highly on the degrees available, and element spacing can be deemed as another source of degrees of freedom. In this paper, we study the joint waveform and element spacing optimization problem. A joint waveform and array optimization criterion is proposed to match the transmit beampattern, the suppression range, and the angular sidelobes, under the constraints of minimal element spacing and total array aperture. Meanwhile, the effect of receive beamforming on suppressing mutual correlation between returns from different spatial directions is also incorporated into the optimization criterion. The optimization problem is solved by the sequential quadratic programming algorithm. Numerical results indicate that with more degrees of freedom from array spacings, colocated MIMO radar achieves a better transmit beampattern matching performance and a lower sidelobe level, compared with a fixed half-wavelength spaced array, but the benefits from additional degrees of freedom from array spacing optimization have a limit.<\/jats:p>","DOI":"10.3390\/s23094375","type":"journal-article","created":{"date-parts":[[2023,4,28]],"date-time":"2023-04-28T10:51:52Z","timestamp":1682679112000},"page":"4375","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Colocated MIMO Radar Waveform-Array Joint Optimization for Sparse Array"],"prefix":"10.3390","volume":"23","author":[{"given":"Jinrong","family":"Yin","sequence":"first","affiliation":[{"name":"Nanjing Institute of Electronic Technology, Najing 210039, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rui","family":"Ma","sequence":"additional","affiliation":[{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingcong","family":"Lin","sequence":"additional","affiliation":[{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shenghua","family":"Zhou","sequence":"additional","affiliation":[{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chen, Y., Wang, S., Luo, Y., and Liu, H. (2023). Measurement Matrix Optimization Based on Target Prior Information for Radar Imaging. IEEE Sens. J.","DOI":"10.1109\/JSEN.2023.3263591"},{"key":"ref_2","unstructured":"Fishler, E., Haimovich, A., Blum, R., Chizhik, D., Cimini, L., and Valenzuela, R. (2004, January 29). MIMO Radar: An Idea Whose Time Has Come. Proceedings of the Radar Conference, Philadelphia, PA, USA."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1109\/MSP.2008.4408448","article-title":"MIMO radar with widely separated antennas","volume":"25","author":"Haimovich","year":"2008","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1109\/MSP.2007.904812","article-title":"MIMO Radar with Colocated Antennas","volume":"24","author":"Li","year":"2007","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1109\/TSP.2005.862813","article-title":"Spatial diversity in radars\u2014Models and detection performance","volume":"54","author":"Fishler","year":"2006","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"638","DOI":"10.1049\/iet-rsn.2010.0153","article-title":"Target statistical correlation characteristic for spatial-frequency jointly diversity MIMO radar","volume":"5","author":"Zhou","year":"2011","journal-title":"IET Radar Sonar Navig."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2091","DOI":"10.1109\/TAES.2016.140900","article-title":"Doppler sensitivity of MIMO radar waveforms","volume":"52","author":"Zhou","year":"2016","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1109\/LSP.2006.877143","article-title":"Optimizing Polyphase Sequences for Orthogonal Netted Radar","volume":"13","author":"Khan","year":"2006","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3126","DOI":"10.1109\/TSP.2004.836530","article-title":"Polyphase code design for Orthogonal Netted Radar systems","volume":"52","author":"Deng","year":"2004","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1109\/TAES.2007.357137","article-title":"MIMO radar waveform design based on mutual information and minimum mean-square error estimation","volume":"43","author":"Yang","year":"2007","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4432","DOI":"10.1109\/TSP.2012.2197615","article-title":"On the design of constant modulus probing signals for MIMO radar","volume":"60","author":"Wang","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4151","DOI":"10.1109\/TSP.2007.894398","article-title":"On probing signal design for MIMO radar","volume":"55","author":"Stoica","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2047","DOI":"10.1109\/TAES.2013.120681","article-title":"MIMO radar range-angular-Doppler sidelobe suppression using random space-time coding","volume":"50","author":"Zhou","year":"2014","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1126\/science.220.4598.671","article-title":"Optimization by simulated annealing","volume":"220","author":"Kirkpatrick","year":"1983","journal-title":"Science"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"5926","DOI":"10.1109\/TSP.2008.929658","article-title":"MIMO Radar Ambiguity Properties and Optimization Using Frequency-Hopping Waveforms","volume":"56","author":"Chen","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3137","DOI":"10.1109\/TAES.2013.120040","article-title":"Detection performance of spatial-frequency diversity MIMO radar","volume":"50","author":"Liu","year":"2014","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_17","unstructured":"Nocedal, J., and Wright, S. (2006). Numerical Optimization, Springer."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1109\/JSTSP.2009.2038981","article-title":"Sparse, Active Aperture Imaging","volume":"4","author":"Schindler","year":"2010","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1049\/iet-rsn.2010.0034","article-title":"Multiple-input multiple-output radar aperture optimisation","volume":"5","author":"Rabideau","year":"2011","journal-title":"IET Radar Sonar Navig."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1049\/iet-rsn.2010.0347","article-title":"Grating lobe control in randomised, sparsely populated MIMO radar arrays","volume":"6","author":"Brennan","year":"2012","journal-title":"IET Radar Sonar Navig."},{"key":"ref_21","unstructured":"Chen, D., Chen, B., and Zhang, S. (2006, January 16\u201319). Multiple-Input Multiple-Output Radar and Sparse Array Synthetic Impulse and Aperture Radar. Proceedings of the IEEE International Radar Conference, Shanghai, China."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Xu, L., Liu, H., Zhou, S., Liu, J., and Yan, J. (2018, January 27\u201331). Colocated MIMO Radar Waveform Design Against Repeat Radar Jammers. Proceedings of the 2018 International Conference on Radar (RADAR), Brisbane, QLD, Australia.","DOI":"10.1109\/RADAR.2018.8557305"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1016\/j.sigpro.2011.08.025","article-title":"Adaptive MIMO radar target parameter estimation with Kronecker-product structured interference covariance matrix","volume":"92","author":"Zhou","year":"2012","journal-title":"Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1109\/TAES.2008.4655353","article-title":"Target detection and parameter estimation for MIMO radar systems","volume":"44","author":"Xu","year":"2008","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zang, H., Liu, H., Zhou, S., and Wang, X. (2012, January 13\u201317). MIMO Radar Waveform Design Involving Receiveing Beamforming. Proceedings of the IEEE International Rada Conference 2014, Lille, France.","DOI":"10.1109\/RADAR.2014.7060447"},{"key":"ref_26","first-page":"1","article-title":"Colocated MIMO radar waveform optimization with receive beamforming","volume":"98","author":"Zhou","year":"2019","journal-title":"Digit. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/9\/4375\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:26:08Z","timestamp":1760124368000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/9\/4375"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,28]]},"references-count":26,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["s23094375"],"URL":"https:\/\/doi.org\/10.3390\/s23094375","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2023,4,28]]}}}